Question

Left over from the big-bang, tiny holes might still wander through the universe. If one with a mass of 1 E 11 kg and a radius of only 1 E -16m reached Earth, at what distance from your head would its gravitational pull on you match that of Earth's.

Answer 1

mass of the given hole, m_h = 1 * 10¹¹ Kg

radius of the hole, r_h = 1 * 10^-16 m

Let my mass be m and the distance of the hole from my head be d when its gravitational pull is equal to that of earth

Gravitational force experienced by me due to earth, F_e

            where g is the acceleration due to gravity on earth, g = 9.8 m/s²

Gravitational force experienced by me due to the hole F_h

For the gravitational pull of the hole on me to match the gravitational pull of the earth on me, the above two forces should be equal, i.e.

d² = 0.6810 m²

d = 0.82 m